For Maggie Scott, it’s all about the stories, and she has plenty to tell. The Boston singer and pianist, now 86, draws most of those stories from the repertoire that’s come to be known as the Great American Songbook — those 20th-century staples written by the likes of Irving Berlin, Cole Porter, the Gershwins, Rogers & Hart, Jerome Kern, Duke Ellington, and Billy Strayhorn. Scott prides herself on her vast repertoire and insists that her students learn it.

“When I first played with her, I was feeling like I didn’t know enough songs to be effective . . . but I was trying really hard,” veteran bassist Marty Ballou says with a laugh. Ballou features Scott once a month in his Monday night gigs at the Top of the Hub. “She’s so connected to the material. It’s not like she’s reading songs; she’s doing songs that are part of her.” (Scott next stops by the Hub to play with Ballou and drummer Jim Gwin on April 6.)

One of the regulars at those shows is local rock luminary and discriminating flaneur Peter Wolf, who has been known to say, “Maggie Scott isn’t just playing the American songbook, she’s living it.”

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“She’s a jewel,” says Wolf. “She knows how to sell a song, and that’s the most important thing. An actor can really make you believe the role they’re playing. The role of the singer is to make the story they’re singing credible and believable. Maggie’s great at that . . . and her piano chops are just out of this world.”

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In fact, Scott began as a pianist. Born in Winthrop, she was smitten with jazz in junior high school, and started going to the big band shows at the RKO Boston Theatre on Washington Street and saw them all: Stan Kenton, the Dorsey Brothers, Gene Krupa, Count Basie, Duke Ellington. “The shows started at 1, and you could stay all day if you wanted to,” she says.

By 18, she was in the musicians’ union, playing lounge piano five or six nights a week. She went to Juilliard for one semester and returned to Boston. And, despite her long tenure at Berklee (since 1978), where she is a revered teacher, she says there’s no substitute for the access she had to live music at the RKO, or for the hands-on experience of learning on the job — “the experience of playing in front of people, and playing what people want to hear.”

In 1950, in her second attempt, Scott won an audition to play the first movement of Gershwin’s “Concerto in F” with the Boston Pops under the discerning baton of Arthur Fiedler. (“It was not easy, believe me.”)

In 1952, she married the bassist Edward Stone, and the two worked for years as a duo. (Stone died in 1974.) She began singing only because audience members kept asking her to. “I thought, OK, I’ll sing a couple of tunes and see what happens. And it seemed OK. I knew how to breathe correctly. And nobody said, ‘Don’t sing.’ ”

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Scott was first drawn to jazz, she says, by the harmonies she heard in those big bands, the chords. “I wanted to know: What was that?,” says Scott.

One of her former students, singing pianist Sarah McKenzie, says that Scott encouraged her to explore harmonic tensions. “She’d say, ‘You’ve got five fingers, Sarah, use all five fingers!’ Put in the ninth and the 11th! Use the extra color!”

At a recent Top of the Hub show, Scott, Ballou, and Gwin offered a particularly rich, swinging instrumental version of the standard “You Stepped Out of a Dream,” by Nacio Herb Brown and Gus Kahn. The crowd at the Hub often uses the excellent nightly jazz as background music, but this one quieted them down, and got enthusiastic applause.

“She played it differently than anyone I’ve played that song with,” says Ballou, pointing out Scott’s use of chord movement over pedal tones. “She plays her own songs her own way.”

And then there’s that singing — simple and straightforward, infallibly swinging, and still beautifully light and pliant. Scott says she favors jazz singers with a “straight” approach — careful attention to phrasing and lyrics, with little or no vibrato: Ella Fitzgerald, Billie Holiday, Carmen McRae, with a caveat for the great Sarah Vaughan’s extravagance.

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Despite her own inventions, Scott is insistent that students learn the tune as written before improvising on it. And there are some songs, she says, “where the melodies and chord progressions are so intricate and beautiful that you shouldn’t mess around with them. ‘Lush Life’ [by Strayhorn] is one of those songs: Sing it the way the man wrote it!”

For “pure” jazz singing, she listens for “an innate sense of time, tempo, and interpretation.”

For his part, Wolf sees Scott as the flagbearer for a tradition. Which is one reason he tries to catch Scott as often as he can. “It’s an opportunity for people to see how it’s done, and how it should be done.”

BONUS TRACKS

If you play your cards right, you can precede Kyle Nasser’s 8 p.m.-midnight sets at the Beat Hotel (see “Noisy Neighbors”) on March 25 with the Miguel Zenón Quartet’s 7:30 show across Harvard Square at the Regattabar. . . . Legendary master percussionist and interdisciplinary performance artist Milford Graves performs and gives the keynote address at the Brandeis Improv Festival (March 27-29). Graves, part of the first wave of free jazz, keynotes a weekend that includes panel discussions and musical and multimedia performances from the likes of pianists Dave Bryant and Tim Ray, saxophonist Tom Hall, bassist Bob Nieske, guitarist Dave Tronzo, Club d’Elf, Jim Guttman’s Klezmer Allstars (with violinist Mimi Rabson), and more. Info at freeimprovisation.com. . . . On April 13, New England Conservatory guru Ran Blake celebrates his 80th birthday (April 20) with his 10th annual film noir concert at NEC’s Jordan Hall, joined by colleague Jason Moran, NEC president Tony Woodcock, and multiple ensembles, reimagining classic scores with video accompaniment.